In the known ignition system (DE-OS No. 27 01 750), a control capacitor is connected in series with a threshold switch in the primary circuit of the ignition system. The capacitor causes the ignition timing discharge to be changed as a function of engine speed. When the ignition current in the primary circuit of the ignition system is blocked at the ignition time, oscillations occur which are coupled back to a control circuit connected to the ignition transistor in such a way that the ignition transistor oscillates back and forth from the blocked into the conductive region. This causes a plurality of sparks to be initiated at the spark plug which is connected to the secondary winding of the ignition coil. Each individual spark only has a duration of approximately 10 to 100 ms. so that the available ignition energy is relatively small.